Alloy Junction 1952 Complete Both Junctions
# Complete Both Junctions: The Junction Isn't Where Dissolution Stopped
Step 25 fixed where each face's dissolution interface came to rest; Step 26 worked out that the acceptor concentration behind that interface isn't uniform, but follows a non-monotonic profile set by the retrograde solidus curve. It is tempting to assume the transistor's actual emitter and collector junctions sit exactly at $x_E$ and $x_C$ — the two dissolution depths Step 6's ceiling equation has tracked since Phase 1. They don't, not quite. A junction is an electrical boundary, not a metallurgical one: it sits wherever the regrown acceptor concentration from Step 26's profile falls to meet the original crystal's background donor concentration, and because that profile rises and falls non-monotonically rather than stepping cleanly from "doped" to "undoped," the electrical junction plane can land measurably short of the metallurgical dissolution depth. Step 27 is where both junctions — emitter and collector — are located precisely, for the first time by electrical definition rather than by depth alone, and where the question first raised by Step 17's placement-asymmetry concern — do the two sides actually end up matching — gets its real answer.
## 1. Where the Profile Crosses the Background
The regrown region is P-type only where the acceptor concentration from Step 26's profile, $N_A(x)$, exceeds the original crystal's N-type background donor concentration, $N_D$ (the same uniform value Step 2 established for the whole boule, long before any of this series's local doping changes began). The electrical junction depth $x_j$ at either face is defined by where the net doping crosses zero — where the two concentrations are equal:
Because $N_A(x)$ — per Step 26's retrograde-solubility profile — rises from a low value near the original dissolution front, climbs to a peak somewhere in the interior where the interface passed through $T_p$, and falls again toward the outer face, equation above can in principle have more than one solution for $x_j$. In practice only the outermost crossing (the one nearest the original crystal surface) matters, because that is the first point, moving inward from where the dissolution interface came to rest, at which the material is still net P-type — everything closer to the surface than that point never accumulated enough acceptor to overcome $N_D$ at all, and is electrically indistinguishable from the original N-type crystal regardless of how much indium metallurgically diffused through it.
## 2. Real Diagram: Metallurgical Depth Versus Electrical Junction
## 3. Matching the Two Faces, and What a Built-In Field Actually Costs
Once each face's electrical junction depth $x_{j,E}$ and $x_{j,C}$ is located, two separate questions converge on the same pair of numbers. The first is geometric and traces straight back to Step 6: the true electrical base width is $W_B \approx t_{\text{slice}} - x_{j,E} - x_{j,C}$, using the electrical depths rather than the raw dissolution depths $x_E$, $x_C$ this series has tracked since Step 20 — and because Step 25's cooling and Step 26's retrograde profile need not treat the emitter and collector faces identically (the same front-to-back asymmetry Step 20 introduced at heating can, in principle, still differ at cooling), $x_{j,E}$ and $x_{j,C}$ are not guaranteed to be equal even when $x_E$ and $x_C$ nearly are. The second question is electrical in its own right: at whatever net doping level the two sides settle on right at $x_j$, the junction supports a built-in potential,
where $n_i$ is germanium's intrinsic carrier concentration at the operating temperature. Because $N_A(x_j)$ is, by the very definition of $x_j$ in Section 1, pinned close to $N_D$ rather than to the much higher peak concentration found deeper in the profile, the built-in potential at the junction itself is set by a comparatively modest net doping ratio — a very different number from what a reading of the profile's peak concentration alone would suggest, and a reminder that the junction's electrical character is governed by conditions right at the crossover, not by how heavily doped the interior of the base happens to be.
## Real Diagram: Two Faces, Compared Side by Side
## Complete Both Junctions's Place in the Process Lineage
Complete Both Junctions follows Step 26, Form the P-Type Regions, which supplied the acceptor concentration profile this step searches for a crossover point; it precedes Step 28, Solidify the Residual Alloy Buttons, which deals with whatever indium-rich liquid remains outside the regrown region once both junctions have been located. It is the second step of Phase 3's final pair and the point where every depth this series has tracked since Step 6 — $x_E$, $x_C$, and now $x_{j,E}$, $x_{j,C}$ — finally resolves into the two electrical boundaries that will define the finished transistor's actual base width and built-in field, rather than the metallurgical depths that have stood in for them since dissolution began.